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A generalization of the product rule for expressing arbitrary-order derivatives of products of functions, where (n; k) is a binomial coefficient. This can also be written ...

The length is the longest dimension of an object.

Likelihood is the hypothetical probability that an event that has already occurred would yield a specific outcome. The concept differs from that of a probability in that a ...

A limb of a tree at a vertex v is the union of one or more branches at v in the tree. v is then called the base of the limb.

A planar diagram depicting a link (or knot) as a sequence of segments with gaps representing undercrossings and solid lines overcrossings. In such a diagram, only two ...

Let F be a differential field with constant field K. For f in F, suppose that the equation g^'=f (i.e., g=intf) has a solution g in G, where G is an elementary extension of F ...

Let rho(x) be an mth degree polynomial which is nonnegative in [-1,1]. Then rho(x) can be represented in the form {[A(x)]^2+(1-x^2)[B(x)]^2 for m even; ...

Given a Lyapunov characteristic exponent sigma_i, the corresponding Lyapunov characteristic number lambda_i is defined as lambda_i=e^(sigma_i). (1) For an n-dimensional ...

An infinite-dimensional differential calculus on the Wiener space, also called stochastic calculus of variations.

A spectrum containing the real numbers larger than Freiman's constant.